**Problem 11** Use the Master theorem to find the asymptotic complexity (Θ) of this function: \[ T(n) = n^4 + T(n) \]**ANSWER:**

Answered: Problem 11 Use the Master theorem to…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Master theorem

The master theorem is a recipe that gives asymptotic estimates for a class of recurrence relations that often show up when analyzing recursive algorithms.

Let a ≥ 1 and b > 1 be constants, let f(n) be a function, and let T(n) be a function over the positive numbers defined by the recurrence

T(n) = aT(n/b) + f(n).

If f(n) = Θ(n^d), where d ≥ 0, then

T(n) = Θ(n^d) if a < b^d,
T(n) = Θ(n^dlog n) if a = b^d,
T(n) = Θ(n^log_ba) if a > b^d.

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